How to animate the creation of a straight line?
I don't have much time here but I think I can help. First make your line, I'm guessing a rectangular prism type shape. You can animate the scaling of it in one direction to show it growing, just make sure you set the origin to the side you don't want to move. (Select the face you want to stay put, then Shift-S and set cursor to selected, then go to object mode and set the origin to the cursor.

I would give a video for reference or something but I'm still figuring this site out, hopefully that was clear enough.